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Hochschild cohomology of a strongly homotopy commutative algebra

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Abstract

The Hochschild cohomology of a DG algebra A with coefficients in itself is, up to a suspension of degrees, a graded Lie algebra. The purpose of this paper is to prove that a certain DG Lie algebra of derivations appears as a finite codimensional graded sub Lie algebra of this Lie algebra when A is a strongly homotopy commutative algebra whose homology is concentrated in finitely many degrees. This result has interesting implications for the free the loop space homology which we explore here as well.

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Authors and Affiliations

  1. Faculté des Sciences, Université de Yaoundé, Yaoundé, Cameroon

    Bitjong Ndombol

  2. Département de mathématique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348, Louvain-La-Neuve, Belgium

    Y. Félix

  3. Département de mathématique, Faculté des Sciences, 2, Boulevard Lavoisier, 49045, Angers, France

    J.-C. Thomas

Authors
  1. Bitjong Ndombol
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  2. Y. Félix
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  3. J.-C. Thomas
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Correspondence to J.-C. Thomas.

Additional information

Bitjong Ndombol and Y. Félix were partially supported by a GEANPYL grant during their stay at the university of Angers. J.-C. Thomas is supported by the CNRS-UMR 6090.

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Ndombol, B., Félix, Y. & Thomas, JC. Hochschild cohomology of a strongly homotopy commutative algebra. manuscripta math. 143, 419–443 (2014). https://doi.org/10.1007/s00229-013-0629-7

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  • DOI: https://doi.org/10.1007/s00229-013-0629-7

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